Tail of a linear diffusion with Markov switching

Benoîte de Saporta 1, 2, 3, 4 Jian-Feng Yao 1, 5
2 CQFD - Quality control and dynamic reliability
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
5 VISTA - Vision spatio-temporelle et active
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
Abstract : Let Y be an Ornstein-Uhlenbeck diffusion governed by a stationary and ergodic Markov jump process X: dY_t=a(X_t)Y_t dt+\sigma(X_t) dW_t, Y_0=y_0. Ergodicity conditions for Y have been obtained. Here we investigate the tail propriety of the stationary distribution of this model. A characterization of either heavy or light tail case is established. The method is based on a renewal theorem for systems of equations with distributions on R.
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Benoîte de Saporta, Jian-Feng Yao. Tail of a linear diffusion with Markov switching. Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2005, 15, pp.922-1018. ⟨10.1214/105051604000000828⟩. ⟨hal-00111278⟩



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